3: the velocity in feet per second of a falling object after v(t)=32t. When will the object be traveling 256 feet per second? 4: Find the equation of a line with a slope of 3 and a point at (0, -8) 5: Two lines: 3X-2y = 2 and -5x+2y = - 10. What are the coordinates of the point where they cross?
3: The velocity of the falling object can be found by substituting the given formula v(t) = 32t. To find when the object will be traveling at 256 feet per second, set v(t) equal to 256 and solve for t:
32t = 256
t = 256 / 32
t = 8 seconds
Therefore, the object will be traveling at 256 feet per second after 8 seconds.
4: The equation of a line with a slope of 3 and passing through the point (0, -8) can be found using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
y - (-8) = 3(x - 0)
y + 8 = 3x
y = 3x - 8
Therefore, the equation of the line is y = 3x - 8.
5: To find the coordinates of the point where the two lines intersect, we need to solve the system of equations given by the two lines:
3x - 2y = 2
-5x + 2y = -10
Adding the two equations eliminates the y variable:
-2x = -8
x = 4
Substitute x back into one of the equations to solve for y:
3(4) - 2y = 2
12 - 2y = 2
-2y = -10
y = 5
Therefore, the coordinates of the point where the two lines intersect are (4, 5).